Quasi-Exactly Solvable Jacobi Elliptic Potential

Ancilla Nininahazwe

doi:10.4236/ojm.2020.103003

Abstract

A new example of 2×2 -matrix quasi-exactly solvable (QES) Hamiltonian which is associated to a Jacobi elliptic potential is constructed. We compute algebraically three necessary and sufficient conditions with the QES analytic method for the Jacobi Hamiltonian to have a finite dimensional invariant vector space. The matrix Jacobi Hamiltonian is called quasi-exactly solvable.

Highlights

Open AccessIn quantum mechanics, the goal consists in computing the eigenvalues of linearHamiltonian
[10] [11] [12] [13] in order to construct a 2× 2 -matrix quasi-exactly solvable (QES) Hamiltonian which is associated to a Jacobi elliptic potential
[10] [11] [12] [13], we apply the QES analytic method in order to construct a new 2× 2 -matrix QES Hamiltonian depending on Jacobi elliptic potential

Summary

Introduction

In few cases, some of which have the eigenvalues found explicitly This type of Hamiltonian is called exactly solvable. [10] [11] [12] [13], the QES analytic method is applied in order to establish a set of three necessary and sufficient conditions for Hamiltonians to have finite dimensional invariant vector spaces. We apply the same QES analytic method established in the Refs. This paper is organized as follows: in Section 2, based on [10] [11] [12] [13], we briefly recall the QES analytic method used to investigate the quasi-exact solvability of 2× 2 -matrix operators.

Nininahazwe DOI

QES Analytic Method

QES Jacobi Hamiltonian

Conclusion